WASHINGTON — Boeing attempted a major step Friday toward getting its 787 Dreamliners flying again, proposing a fix for the plane’s troubled batteries that could allow flights to resume as early as April, congressional officials said.

The next question is whether the Federal Aviation Administration will agree to let the planes fly even though the root cause of a battery fire in one plane and a smoking battery in another is still unknown.

A Boeing team led by chief executive Ray Conner presented the plan to FAA head Michael Huerta. The airliners, Boeing’s newest and most technologically advanced, have not been allowed to fly since mid-January.

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The plan — a long-term solution, rather than a temporary fix — calls for revamping the aircraft’s two lithium ion batteries to ensure that any short-circuiting that could lead to a fire won’t spread to other battery cells, officials said.

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